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162/.2 = 810

Because .2 goes into 162, 810 times

Of course, thanks Bob, my logic was fine I just didn't read the question properly.  

I didn't realise that the 2 groups of five were studying different subjects. 

Thank you very much :))

Even after you answered it took me ages to realise that I had just not read the question properly.   

Could you please say if my answer would have been right if the there had been no different subjects involved, so that order would not matter. ??  I think it seems right but I am not at all sure ://        

1) No domain restrictions on the first one. It is a standard 4th degree polynomial.

What do you mean? 

333 333 333  is a nine digit number made or 3s

or

3^3*3*3*3*3*3*3*3**3*3*3*3*3^3= 387 420 489 

is a 9 digit number made from 3s 

Which do you have in mind?

1. 9a+2b-8a-3b

To make things easier, put like terms together (so according to their unknown).

  9a+2b-8a-3b ≡ 9a-8a+2b-3b

Now you can easily see what to subtract, and what to add.

  9a-8a+2b-3b

eg: 9a-8a = 1a (or 'a')

      2b-3b = -1b (or '-b')

Which means the simplified format for 9a+2b-8a-3b is a-b.

2. 9a+5b+7a+8b

ans = 16a+13b

"ax-y=-3b

9ay-36x=-ab4

If a ≠ 0 and b ≠ 0

What values of a and b do the equations become:

a. inconsistent

b. consistent and dependent

c. consistent and indepent"

.

Try:  http://mathworld.wolfram.com/PrincipalSquareRoot.html 

What do you want done with this.

In base 10 it is    6.60076229337E+33

Where is written?

Thank you Geno,
but is there somewhere to read?

  ?

I get a slightly different answer than the guest does

Notice that  the  greatest possible average from  adding the digits  2 + 4 + 6 + ....+ n

is given by :

[ ( n / 2) (n / 2  + 1 ) - 2 ]  /   [ (n - 2) / 2 ]

Example....   2 , 4 , 6 , 8  10 

And the greatest  average possible average is produced when the least number, 2, is omitted

And this average is   [ ( 10 / 2) (10 / 2  + 1 ) - 2 ]  /   [ (10 - 2) / 2 ]  =

[(5)(6) - 2] / (8 / 2 )  =  28 / 4  =  7

So...we want to solve this :

[ ( n / 2) (n / 2  + 1 ) - 2 ]  /   [ (n - 2) / 2 ]  =  28      simplify

 2 [ n^2 / 4  +  n/2  - 2 ] =   28 [ n - 2 ]

2 [ ( n^2 + 2n - 8) / 4 ]  =  28 [n - 2]

( n^2 + 2n - 8) / 2  = 28 [n - 2]

( n^2 + 2n - 8) =  56 [n - 2]

n^2 + 2n - 8 =  56n - 112

n^2 - 54n + 104  = 0     factor

( n - 52) ( n - 2)  = 0

And its obvious that  n  = 52  and this is the smallest value of n

Proof :

2  +   4  +   6  +  ....... +  52     can be written as

1   +  2   +  3 +  ........ +  26

+

1   +  2   +  3  + ......... + 26

So  52  is the 26th term

And  the sum of these two series  =  2 (26)(27)/ 2  =  26 * 27

And the average of this series omitting the first term is given by

[Series sum -  2] / [ Number of remaining terms omitting the first one, 2 ] 

[ 26 * 27 - 2 ] / 25  =

[ 702 - 2] / 25  =

700 / 25  =

28

I take the first 10 digits to be the first 10 from the right.  Given this definition then the answer will be 0000000000

cos 46°  =  b / 120

120 cos 46°  =  b

b  ≈  83.359  km / hr

If you meant (10^12)! =1,000,000,000,000!, then that is a different question. Fortunately, the mighty

Wolfram/Alpha can compute the first dozens of digits directly. So:

(10^12)! =1.40366116037375609072013386771345056395992457... × 10^11565705518103

So the number begins with: 1403661160373.........etc.

10¹  =  10

10²  =  100

10³  =  1000

...

Thus, the first 10 digits of  10^12!  =  1 000 000 000  ...

0.47  +  0.2    =    0.47  +  0.20    =    0.67

There are two square roots of 4:  2  and  -2.

The positive square root is called the "principal root".

The square root sign is defined to mean the principal root; thus, sqrt(4) = 2, not -2.

I've looked at this one for a bit......I'm not sure that the second sequence is an arithmetic one......more like a "constant" one

Here's my reasoning

If the second term of the first sequence is the first term of the first sequence plus the first term of the second sequence.....since the first term of the first sequence is 0, the second term must just be the common difference between terms of that series.....call it "d"

But this means that the first term of the second sequence must be "d"

Let the common difference of the second sequence be "e"

So.....since the 5th term of this sequence is 3, then the first term, d,  must equal  3  - 4e....so  d  =  3 - 4e  (1)

And the third term of the first sequence is the second term of the first sequence, d, plus the second term of the second sequence, 3 - 3e....so....the third term of the first sequence, 2d, must equal d  + ( 3 - 3e)   =  2d.......so......subbing (1)  into this we have that   (3 - 4e) + (3 - 3e)   =  2d  ⇒    6 - 7e  = 2 (3 - 4e)  ⇒    6  - 7e  = 6 - 8e    which implies that  e = 0

So.........the second sequence must be constant....and the 5th term of the first series must be 0 + 4(d)  =

0 + 4(3)  =  12

Here are the two  sequences

0    3    6      9      12

3    3    3      3       3

Anyone else have any other thoughts  ??

35 000 000 d'habitants diviser 9 984 670 km

35,000,000 / 9,984,670 =~3.5 People per square km in Canada !!.

3^7,625,597,484,987

=1.2580142906 2749131786 0390698.................. x  10^3,638,334,640,024

Since the set consists of even integers from: 2, 4,  6, 8.........n, and if the average of the set is 28, then 28th term must be=28 x 2 =56=n. The sum of 28 terms from 2+4+ 6+ 8.......56=812. 812/28 =29 average. Therefore: 812 - 56 =756 / 27=28 - the average.

Therefore, the least possible value of n = 56. 

3^7625597484987 = infinity

Pi is the ratio of the circumference of a circle to the circle's diameter. Basically, a circle's diameter can stretch around the circle pi times.

Pi is approximately equal to 3.141592, but it has infinitely many digits following the decimal point

1) Add 16 to both sides of the equation

\(16=8z\)

2) Divide both sides of equation by 8 to find z

\(2=z\)

4-(-3)=4+3=7

The reason it's like adding is because -1*-3=3, so -(-3) = 3

25 - (y+3 )= 10     apply the negative over the terms in the parentheses

25 - y - 3   = 10      combine like terms  on the left side

22  - y   = 10          add y to both sides, subtract 10 from both sides

12  = y